


import numpy as np
import skfuzzy as fuzz

if __name__ == "__main__":
   # Create universe of discourse in Python using linspace ()
   lowerCamelCase__							:						List[str]							     =   np.linspace(start=0, stop=7_5, num=7_5, endpoint=True, retstep=False)

   # Create two fuzzy sets by defining any membership function
   # (trapmf(), gbellmf(), gaussmf(), etc).
   lowerCamelCase__							:						List[str]							     =   [0, 2_5, 5_0]
   lowerCamelCase__							:						Any							     =   [2_5, 5_0, 7_5]
   lowerCamelCase__							:						Optional[int]							     =   fuzz.membership.trimf(X, abca)
   lowerCamelCase__							:						Optional[Any]							     =   fuzz.membership.trimf(X, abca)

   # Compute the different operations using inbuilt functions.
   lowerCamelCase__							:						List[Any]							     =   np.ones(7_5)
   lowerCamelCase__							:						Dict							     =   np.zeros((7_5,))
   # 1. Union = max(µA(x), µB(x))
   lowerCamelCase__							:						List[Any]							     =   fuzz.fuzzy_or(X, young, X, middle_aged)[1]
   # 2. Intersection = min(µA(x), µB(x))
   lowerCamelCase__							:						int							     =   fuzz.fuzzy_and(X, young, X, middle_aged)[1]
   # 3. Complement (A) = (1- min(µA(x))
   lowerCamelCase__							:						Dict							     =   fuzz.fuzzy_not(young)
   # 4. Difference (A/B) = min(µA(x),(1- µB(x)))
   lowerCamelCase__							:						str							     =   fuzz.fuzzy_and(X, young, X, fuzz.fuzzy_not(middle_aged)[1])[1]
   # 5. Algebraic Sum = [µA(x) + µB(x) – (µA(x) * µB(x))]
   lowerCamelCase__							:						str							     =   young + middle_aged - (young * middle_aged)
   # 6. Algebraic Product = (µA(x) * µB(x))
   lowerCamelCase__							:						Union[str, Any]							     =   young * middle_aged
   # 7. Bounded Sum = min[1,(µA(x), µB(x))]
   lowerCamelCase__							:						List[Any]							     =   fuzz.fuzzy_and(X, one, X, young + middle_aged)[1]
   # 8. Bounded difference = min[0,(µA(x), µB(x))]
   lowerCamelCase__							:						Any							     =   fuzz.fuzzy_or(X, zero, X, young - middle_aged)[1]

   # max-min composition
   # max-product composition

   # Plot each set A, set B and each operation result using plot() and subplot().
   from matplotlib import pyplot as plt

   plt.figure()

   plt.subplot(4, 3, 1)
   plt.plot(X, young)
   plt.title("""Young""")
   plt.grid(True)

   plt.subplot(4, 3, 2)
   plt.plot(X, middle_aged)
   plt.title("""Middle aged""")
   plt.grid(True)

   plt.subplot(4, 3, 3)
   plt.plot(X, union)
   plt.title("""union""")
   plt.grid(True)

   plt.subplot(4, 3, 4)
   plt.plot(X, intersection)
   plt.title("""intersection""")
   plt.grid(True)

   plt.subplot(4, 3, 5)
   plt.plot(X, complement_a)
   plt.title("""complement_a""")
   plt.grid(True)

   plt.subplot(4, 3, 6)
   plt.plot(X, difference)
   plt.title("""difference a/b""")
   plt.grid(True)

   plt.subplot(4, 3, 7)
   plt.plot(X, alg_sum)
   plt.title("""alg_sum""")
   plt.grid(True)

   plt.subplot(4, 3, 8)
   plt.plot(X, alg_product)
   plt.title("""alg_product""")
   plt.grid(True)

   plt.subplot(4, 3, 9)
   plt.plot(X, bdd_sum)
   plt.title("""bdd_sum""")
   plt.grid(True)

   plt.subplot(4, 3, 1_0)
   plt.plot(X, bdd_difference)
   plt.title("""bdd_difference""")
   plt.grid(True)

   plt.subplots_adjust(hspace=0.5)
   plt.show()




lowercase			:				Dict   =     [sum(int(c, 10) ** 2 for c in i.__str__()) for i in range(10_00_00)]






def        snake_case__		(    lowerCamelCase_		):
							A      :					List[str]      		=					0
							while number:
														# Increased Speed Slightly by checking every 5 digits together.
														sum_of_digits_squared += DIGITS_SQUARED[number % 100000]
														number //= 100000

							return sum_of_digits_squared


# There are 2 Chains made,
# One ends with 89 with the chain member 58 being the one which when declared first,
# there will be the least number of iterations for all the members to be checked.

# The other one ends with 1 and has only one element 1.

# So 58 and 1 are chosen to be declared at the starting.

# Changed dictionary to an array to quicken the solution
lowercase			:				list[bool | None]   =     [None] * 10_00_00_00
lowercase			:				int   =     True
lowercase			:				Tuple   =     False






def        snake_case__		(    lowerCamelCase_		):

							if CHAINS[number - 1] is not None:
														return CHAINS[number - 1]  # type: ignore

							A      :					int      		=					chain(next_number(lowerCamelCase_		)		)
							A      :					Dict      		=					number_chain

							while number < 10000000:
														A      :					Any      		=					number_chain
														number *= 10

							return number_chain






def        snake_case__		(    lowerCamelCase_ = 10000000		):
							for i in range(1     ,				lowerCamelCase_		):
														if CHAINS[i] is None:
																					chain(i + 1		)

							return CHAINS[:number].count(lowerCamelCase_		)


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		print(F"{solution() = }")






